Fingering Instabilities of Driven Spreading Films

Troian, Sandra M.; Herbolzheimer, E.; Safran, S. A.; Joanny, Jean‐François

doi:10.1209/0295-5075/10/1/005

Cited by 317 publications

(326 citation statements)

References 12 publications

Supporting

Mentioning

287

Contrasting

Order By: Relevance

“…[20][21][22] The reader is referred to these references for an in depth discussion. This mechanism is quite different, however, from the fingering behavior observed at the leading edge of other free surface spreading problems, like the flow down an inclined plane 30,31 or the thermocapillary driven spreading of a thin liquid film. 32,33 In these other spreading processes, the instability occurs right at the leading edge and causes the spreading front to separate into long narrow rivulets which never undergo spreading, shielding, or tip-splitting.…”

Section: A Linearized Transient Responsementioning

confidence: 61%

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Matar

Troian

1999

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We describe the response of an insoluble surfactant monolayer spreading on the surface of a thin liquid film to small disturbances in the film thickness and surfactant concentration. The surface shear stress, which derives from variations in surfactant concentration at the air-liquid interface, rapidly drives liquid and surfactant from the source toward the distal region of higher surface tension. A previous linear stability analysis of a quasi-steady state solution describing the spreading of a finite strip of surfactant on a thin Newtonian film has predicted only stable modes. ͓Dynamics in Small Confining Systems III, Materials Research Society Symposium Proceedings, edited by J. M. Drake, J. Klafter, and E. R. Kopelman ͑Materials Research Society, Boston, 1996͒, Vol. 464, p. 237; Phys. Fluids A 9, 3645 ͑1997͒; O. K. Matar Ph.D. thesis, Princeton University, Princeton, NJ, 1998͔. A perturbation analysis of the transient behavior, however, has revealed the possibility of significant amplification of disturbances in the film thickness within an order one shear time after the onset of flow ͓Phys. Fluids A 10, 1234 ͑1998͒; ''Transient response of a surfactant monolayer spreading on a thin liquid film: Mechanism for amplification of disturbances,'' submitted to Phys. Fluids͔. In this paper we describe the linearized transient behavior and interpret which physical parameters most strongly affect the disturbance amplification ratio. We show how the disturbances localize behind the moving front and how the inclusion of van der Waals forces further enhances their growth and lifetime. We also present numerical solutions to the fully nonlinear 2D governing equations. As time evolves, the nonlinear system sustains disturbances of longer and longer wavelength, consistent with the quasi-steady state and transient linearized descriptions. In addition, for the parameter set investigated, disturbances consisting of several harmonics of a fundamental wavenumber do not couple significantly. The system eventually singles out the smallest wavenumber disturbance in the chosen set. The summary of results to date seems to suggest that the fingering process may be a transient response which nonetheless has a dramatic influence on the spreading process since the digitated structures redirect the flux of liquid and surfactant to produce nonuniform surface coverage. © 1999 American Institute of Physics. ͓S1054-1500͑99͒02001-7͔ Surfactant molecules play a vital role in many biological and industrial processes because of their native ability to lower surface tension in proportion to their concentration. Their presence greatly improves the wetting and spreading capability of commonplace substances like inks, paints, and herbicides. Lung surfactants produced in the alveoli are critical in maintaining lung compliance. A deficiency in lung surfactant production, for example, is known to cause pulmonary edema and other respiratory difficulties. When surfactant molecules contact a liquid surface of higher surface tension, a shear stress develops...

show abstract

Section: A Linearized Transient Responsementioning

confidence: 61%

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Matar

Troian

1999

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…The limitR → ∞ for both flow down the outside and inside of a cylinder corresponds to the very well studied equation for flow down a vertical plane (α = π/2) [1,4,5,7,18]. By observing that β = 0 removes substrate curvature completely from the model (1), we use this value of β as a 'control' against which we compare our results for β = 1 (outside a cylinder) and −1 (inside a cylinder).…”

Section: C379mentioning

confidence: 99%

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

Mayo

McCue

Moroney

2013

ANZIAMJ

View full text Add to dashboard Cite

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is the effect the curvature of the cylinder has on the gravity driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further,

show abstract

“…Our model is also analogous to that describing the flow of thin fluid films sliding down an inclined plane. Adopting the lubrication approximation [46,50,77,49,18], the evolution equation of the film height h can be written as…”

Section: Related Models In Fluid Mechanicsmentioning

confidence: 99%

“…For completely wetting fluids, Troian et al [77] proposed to model the contact line dynamics by assuming a precursor film of (small) thickness b downstream of the front. In our context, this precursor film corresponds to the initial water saturation.…”

Section: Related Models In Fluid Mechanicsmentioning

confidence: 99%

“…The model predicts a saturation overshoot at the tips of the fingers, a feature that is believed to be essential for the instability of the infiltration front [70,42,30,71,31]. The mathemat-ical structure of the model is analogous to that describing the flow of thin films and driven contact lines [50,77,49,18,86,52,27,26,75,44,53], and to phase-field models of epitaxial growth of surfaces, binary transitions and solidification [21,22,19,40].…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

Cueto‐Felgueroso

Juanes

2009

Journal of Computational Physics

View full text Add to dashboard Cite

This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebyshev pseudo-spectral method, due to its slow convergence in problems where the solution has steep internal layers. We discuss the effectiveness and conditioning of the proposed discretization, and show that it allows the computation of accurate traveling waves and eigenvalues for small values of the initial water saturation/film precursor, several orders of magnitude smaller than the values considered previously in analogous stability analyses of thin film flows, using just a few hundred grid points.

show abstract

Fingering Instabilities of Driven Spreading Films

Cited by 317 publications

References 12 publications

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

Contact Info

Product

Resources

About